Basically book value = assets - liabilities, so as you say, in principle there is nothing wrong with a negative book value ("shareholder's deficit").

In principle "book value" would be the value of a company to shareholders if all liabilities were paid off. The "in principle" comes because it probably isn't so; equipment and inventory likely would have to be sold for less than the value on the books, other things may sell for more (e.g. sometimes real estate, purchased companies).

Ben Graham says that book value is more accurately a measure of the money "put into" a company (shareholder's equity = money from issued stock + paid in capital + retained earnings - treasury stock, possible I'm missing one or two things but these are the main ones). One can make this number negative by paying out quite a bit of equity (e.g. special dividend) or buying back a bunch of shares. The times I have seen it has been the latter (take on debt to buy back a lot of shares).